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Energy stability of the Ekman boundary layer

Published online by Cambridge University Press:  29 March 2006

Joseph J. Dudis  and
Stephen H. Davis
Joseph J. Dudis
Affiliation:
The Johns Hopkins University, Baltimore, Maryland
Stephen H. Davis
Affiliation:
The Johns Hopkins University, Baltimore, Maryland
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Abstract

The critical value RE of the Reynolds number R is predicted by the application of the energy theory. When R < RE, the Ekman layer is the unique steady solution of the Navier-Stokes equations and the same boundary conditions, and is, further, stable in a slightly weaker sense than asymptotically stable in the mean. The critical value RE is determined by numerically integrating the relevant Euler-Lagrange equations. An analytic lower bound to RE is obtained. Comparisons are made between RE and RL, the critical value of R according to linear theory, in order to demark the region of parameter space, RE < R < RL, in which subcritical instabilities are allowable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 47 , Issue 2 , 31 May 1971 , pp. 405 - 413
Copyright
© 1971 Cambridge University Press

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References

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